I've actually managed to twist the frayed ends of a cable back together and slide an end cap onto the end on more than one occasion. It requires a bit of patience and dexterity, but it's not terribly difficult.
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jimirings♦Jun 1 '13 at 16:21

Those end-caps are quite reusable. If you take a pair of pliers and squeeze it gently so that the flattened portion opens up you can then slide it back onto the cable. Using the pliers you can then re-crimp it on the cable. Although it looks ugly and everyone will know that you are too cheap to buy a 10c end-cap.

A little bit of superglue placed at the end of the cut seems to help keep the individual wires from separating.

His problem is that it's already too frayed to easily get another cap on. A reused one will be harder to get on.
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armbMay 29 '13 at 9:28

"What would work as a suitable replacement for a cap?" - OP. There are other concerns in his post, but his direct question is about a replacement cap and if superglue will work.
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Ritch MeltonMay 29 '13 at 14:04

This is good information, but as the other users note, the cable end is too frayed to get another cap onto.
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Robert DouganMay 30 '13 at 8:47

Another option is a bit of tin soldering wire: give it a couple of tight loops around the end of the cable then squash it with pliers. Tin is soft enough to be defformed around the cable without deforming the cable.

Yet another option is to use an actual soldering iron to cover the very last centimeter of cable with tin. It is quite difficult to solder the end of the already installed cable though.

If the cable is not too badly frayed it can be de-frayed with pliers, grabbing all the strands and twisting it in the right direction. Do it before applying the cap end substitute.

My experience with soldering is that most cables are impregnated with some kind of lubrification which makes soldering practically impossible. Would be the cleanest option if it worked, though...
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sarnuJun 7 '13 at 10:07

Well, it worked for me, I gues the soldering gun burned the oil quite well. If that doest't work, maybe a lighter can do it. I also remember having bought cables that came with a fused end, something like it was heated with a torch or soething like that and just when the cable got softened it was squeezed so the strands would keep together...
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JahazielJun 10 '13 at 21:40

I've used a cable crimp. It looked terrible but it prevent the cable from unravelling before I got to the bike shop to discover that a bike shop will usually give you those end caps if you buy something else from the store. The shops have them in the thousands and they probably paid about $3 for them.